edge impurity transport study in stochastic layer of lhd and scrape-off layer of hl-2a

6th Japan Korea workshop 28-29 July 2011, NIFS, Toki-city Japan

Edge impurity transport study in stochastic layer of LHDand scrape-off layer of HL-2A

1

M. Kobayashi, S. Morita, C.F. Dong, Y. Feng*, S. Masuzaki, M. Goto, T. Morisaki, H.Y. Zhou, H. Yamada and the LHD experimental group

National Institute for Fusion Science, Toki 509-5292, Japan*Max-Planck-Institute fuer Plasmaphysik, D-17491 Greifswald, Germany

Z.Y. Cui, Y.D. Pan, Y.D. Gao, J. Cheng, P. Sun, Q.W. Yang and X.R. DuanSouthwestern Institute of Physics, P. O. Box 432, Chengdu 610041, China

1. Introduction

2. Edge impurity transport and energy transport

3. Modelling results of LHD & HL-2A

Effects of magnetic field geometry

4. Summary

Contents


Introduction : Impurity transport in SOL/DivertorUnderstanding of impurity transport in SOL/Divertor region is important for control ofImpurity influx to core, Radiation distribution & intensity in SOL, Material migration.

2

Effects of the different magnetic field geometry on the edge

impurity transport?

Divertor optimization for fusion reactor is ongoing in tokamaks (2D), stellarators, non-axisymmetric tokamaks (3D).

e.g. Ergodic divertor in TEXT, Tore Supra, TEXTOR-DED,DIII-D etc.

Stochastic field as a tool for controlling edge plasma

3D divertor configuration intrinsic edge stochastization

Helical devices with non-axisymmetric configurationITER: Tokamak

2D axi-symmetric SOL(Closed, V-shaped divertor)


//-Impurity transport model ↔ Ion energy transport

Momentum : // - Classical force balance

Friction

....1

71.06.2 //22//////

s

nT

nZeE

s

TZ

s

TZ

VVm

t

Vm zi

z

ei

s

ziz

zz

Ion thermal force Electric field

Impurity pressure gradient force

score SOL

LCFS

targ

et

Ti

dTi/ds

ViII

Recycling

Thermal

Friction

3

Electron thermal force

s

T

m

ZVV i

z

si

impZ

2////

6.2

In a steady state

iD

iV

ii

i

iii

i

z

s

i

q

q

s

TT

VTn

s

T

m

Z

V

//

//

5.20

//

2// 2

5

6.2

The force balance is closely related to ion energy transport.

Extra function is added to energy transport module of EMC3-EIRENE to analyze the energy transport.


4

• Dz is same as the value of bulk plasma (which is deduced from experiments).• Dz has No charge dependence. No drift.

Mass : ⊥- Diffusion with anomalous coefficient

zzzzzzzzzzzz

zzzz

nRnRnSnS

nbbDbVn

111111

//

Ionization, recombination

Diffusion

Source at PFC :• Divertor plate or first wall with 0.05 eV ejection energy.

Simplification for perpendicular transport model


5

3D modelling of LHD edge region (EMC3-EIRENE)

Boundary conditionsBohm condition at divertor platesPower entering the SOLDensity on LCMSSputtering coefficient

SOLPSOL

Core plasma

LCMS

wall

targ

et

EMC3

Div

erto

rle

gs

C0

H,H2

Computational mesh, configuration and installations Core, CX-neutral transport, particle source SOL, EMC3 simulation domainVacuum of plasma*

Cross-field transport coefficients e=i=3D roughly holdsspatially constant (global transport) determined experimentally

Example of LHD helical divertor

Physics modelStandard fluid equations of mass, momentum, ion and electron energyTrace impurity fluid model (Carbon)Kinetic model for neutral gas (Eirene)


-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2 2.5 3 3.5 4 4.5 5 5.5 6

vessel_162

C

B

6

divertor plate

Helical coils

R=3.90 ma~0.70 m

LHD

HL-2A

LHD heliotron and HL-2A tokamak : distinct magnetic flux tube topology

R=1.65 ma= 0.40 m

105 104 103 102 101 100

Connection length (m)

1 m

1 m

Stochastic layerLC=10 m~1km

Scrape-off layer

LC~40 m

Divertor plate

Divertor plate

Divertor legs

Separatrix

R

Z

Enhanced interaction ⊥between flux tubes

Dominant // transportdivertor entrance


7

10-1

100

101

100

101

102

103

0 10 20 30

PARA_DATA_NUP050_50+-05m_out

nz/nzd Spz(A/m**3)

s (m)

(c) nimp / nimp_down

Sp imp (A/m3)

-1 105

0

1 105

0 10 20 30

PARA_DATA_NUP050_C1_50+-05m_out

Ther_e(m/s)Ther_iFricE//Vimp

s (m)

//V

(105

m/s

)

0

4

-4

theV//thi

V//

fricV//E

V//

imp

ZV

//(b)

(MW

/m2)

//q

=0.3x1019 m-3LCFSn

e

Dq//i

Dq//

i

Vq//

e

Vq//

-2

-1

0

0 10 20 30

PARA_DATA_NUP050_50+-05m_out

COND_e(MW/m**2)COND_iCONV_eCONV_i

s (m)

(a)

Divertor plate X-point

-1

-0.5

0

0.5

1 1.5 2

trace_outers 17:42:11 2011/03/26

C

Z

C

ZZ (m

)

R (m)

0 m

510

15

202530

35

40

45

50 m

R

Z

Divertor plates

Low density (collisionality) case : HL-2AStrong thermal force ( )

Impurity buildup at upstream

iV

iD qq ////

Coordinate s


8

-3

-2

-1

0

0 10 20 30


COND_e(MW/m**2)COND_iCONV_eCONV_i

s (m)

=0.6x1019 m-3LCFSn

(MW

/m2)

//q

(d)

-2 104

-1 104

0

1 104

2 104

0 10 20 30


Ther_e(m/s)Ther_iFricE//Vimp

s (m)

//V

(104

m/s

)

0

2

-2

(e)

10-2

10-1

100

100

101

102

103

0 10 20 30


nz/nzd Spz(A/m**3)

s (m)

Sp imp (A/m3)

nimp / nimp_down

(f)

-1

-0.5

0

0.5

1 1.5 2

trace_outers 17:42:11 2011/03/26

C

Z

C

ZZ (m

)

R (m)

0 m

510

15

202530

35

40

45

50 m

R

Z

Divertor plates

High density (collisionality) case : HL-2A Strong friction force near divertor ( )

Impurity screening (against divertor source) Residual thermal force at upstream ( )

iV

iD qq ////

iV

iD qq ////

e

Dq//i

Dq//

i

Vq//

e

Vq//

theV//thi

V//

fricV//E

V//

imp

ZV

//

Divertor plate

Coordinate s


999

Magnetic field structure in LHD (Large Helical Device)LHD

Helical coilsConnection length (LC) distribution in poloidal cross section

3.9 m

radial

poloidal10/8

10/710/6

10/2

10/3

10/4

10/5

Mode structure n/m

Edge surface layers*

Stochastic region*

reff (m)

0.70

0.65

0.60

Divertor

Core plasma


10

radial

poloidal


Stochastic region*

reff (m)

0.70

0.65

0.60

Divertor

Core plasma

10-1

100

101

102

1 100 1 101 1 102 1 103 1 104

P08_D0.50_SHI1.50_C1_NUP2.0_DP3DT3dt1e-9_LCSPEC 14:46:29 2011/05/04

e_cond_p_w(MW/m**2)e_conv_p_wi_cond_p_wi_conv_p_w

LC (m)

i=52

reff=0.72 m(M

W/m

2 )//q

10-1

100

101

102

1 100 1 101 1 102 1 103 1 104



LC (m)

i=12

reff=0.65 m

(MW

/m2 )

//q

LC (m)104103102101100

10-1

100

101

102

1 100 1 101 1 102 1 103 1 104



LC (m)

i=12

reff=0.60 m

(MW

/m2 )

//qe

Dq//

i

Dq//

i

Vq//

e

Vq//

Upstream

Downstream

Low density (collisionality) case : LHDStrong thermal force ( )

Impurity buildup at upstream

-10

-5

0

5

10

0.6 0.65 0.7

P08_D0.50_SHI1.50_C1_NUP2.0_DP3DT3_RPRF_PRE

fric(e4m/s)e_thermi_thermE//_Z=3F_BAL

reff (m)

theV//thi

V//

fricV//E

V//

imp

ZV

//

=2.0x1019 m-3LCFSn

//V

(104

m/s

)

(a)

10-1

100

10-4

10-3

10-2

10-1

0.6 0.65 0.7


nz/nzd Sp_imp(e22/s/m**3)

reff (m)

nimp/nimp_down

Sp imp

(1022/s/m3)(b)

Radial impurity profile

iV

iD qq ////

DivertorCore plasma


10-1

100

101

102

1 100 1 101 1 102 1 103 1 104

P08_D0.50_SHI1.50_C1_NUP5.0_DP3DT3_LCSPEC 14:52:26 2011/05/04


LC (m)

i=52

LC (m)104103102101100

reff=0.72 m

11

radial

poloidal


Stochastic region*

reff (m)

0.70

0.65

0.60

e

Dq//

iDq//

i

Vq//

e

Vq//

Upstream

Downstream

10-1

100

101

102

1 100 1 101 1 102 1 103 1 104



LC (m)

i=30

reff=0.65 m

10-1

100

101

102

1 100 1 101 1 102 1 103 1 104



LC (m)

i=12

reff=0.60 m

(MW

/m2 )

//q(M

W/m

2 )//q

(MW

/m2 )

//qHigh density (collisionality) case : LHDStrong friction force @ downstream ( )Impurity screeningSuppression of thermal force at upstream ( )

iV

iD qq ////

iV

iD qq //// ~

-4

-2

0

2

4

0.6 0.65 0.7


fric(e4m/s)e_thermi_thermE//_Z=3F_BAL

reff (m)

//V

(104

m/s

)

=5.0x1019 m-3LCFSn

(c)

10-1

100

10-4

10-3

10-2

10-1

0.6 0.65 0.7


nz/nzd Sp_imp(e22/s/m**3)

reff (m)

(d)

Radial impurity profile

Divertor

Core plasma

DivertorCore plasma


12

0.1

1

10

0.1 1 10

LHD_model_Tu_nu_Td_nd_div_source

LHD div sourceLHD wall sourceHL-2A div sourceHL-2A wall source

nuSOLi*ion

SOL

*

imp

dowm

imp

LCFSn

n/

HL-2A

LHD

Divertor sourceWall source

Scr

eeni

ng

Impurity screening as a function of and impurity source locationion

SOL

*

HL-2A: very strong screening against divertor source, but weak against first wall sourceLHD: modest screening against divertor source, but effective against first wall too

Geometrical effect


13

100

101

102

103

10-1 100 101 102

papra-perp_analytical_model 18:11:08 2011/07/13Te,i (eV)Te,i (eV)Te,i (eV)Te,i (eV)TiTiTiTiTiTiTiTiTiTiTiTiTiTin

e (1019 m-3)

ion

10-3

10-2

10-1

HL-2A

LHD

q //=q⊥

for =10-4

(b)

Edge plasma parameter range of LHD and HL-2A(effects of perpendicular transport)

HL-2A: high density and low temperature at downstream because of strong up-down coupling through SOL flux tubes

LHDHL-2A

32 , updownupdown nnnT

Preferable for increasing ratio iD

iV qq //// /

LHD: enhanced perpendicular transport in stochastic layer weakens the up-down coupling

5.11, udud nnnT

Modest change of at downstreamiD

iV qq //// /

qq//

qq ~//


14

10-2

10-1

100

101

102

0.6 0.65 0.7

FLUX_1e19_25eV_375_100000pa

Para/Perp_iPara/Perp_iPara/Perp_iPara/Perp_i

reff (m)

25eV

50eV

100eV

200eV

ion

i

D

i

Dq

q

///

(b)

Enhanced perpendicular transport in stochastic layer of LHD can replace withsuppression of thermal force at upstream

iDq//

iDq

Radial profiles of ion energy transport ratio between // and components in LHD⊥


15

3 12 0 -1 -2 -3Friction – Thermal force (104 m/s)

Friction force

dominant

Thermal force

dominant

nLCFS=5.0x1019 m-3

LHD

nLCFS=0.59x1019 m-3

HL-2A

Distribution of screening region in LHD and HL-2A

Residual thermal force

Flow acceleration Flow acceleration

No flow acceleration

LHD: Screening region distributed poloidally screening effect is independent of impurity source location

HL-2A: Screening region localized near divertor plate screening effect is very sensitive to impurity source location

Inclusion of large upstream flow observed in experiments might alter the results


Summary

Modelling resultsThe modelling shows impurity screening for the both devices.

The screening effect is different between the both devices against collisionality (density) and impurity source location. HL-2A: Very strong screening against divertor source, but not for first wall source LHD: Modest screening against divertor source, but screening effective against first wall too

Magnetic field geometrical effect

InterpretationHL-2A: Strong up-downstream coupling

Preferable for increasing ratio at downstream, i.e. screening. No flow acceleration at upstream

weak against first wall source Inclusion of large upstream flow acceleration in experiments might alter the results

LHD: Enhanced transport in stochastic layer⊥ weaken up-down coupling modest screening effect compared to HL-2A can replace with reduction of thermal force ( )

Screening region is distributed poloidally screening effect independent of impurity source location

Validation of the model results in experiments is ongoing …….. 16

Edge impurity transport has been analyzed in LHD and HL-2A based on fluid impurity transport model using 3D edge transport code EMC3-EIRENE.

iD

iV qq //// /

iDq//

iDq

iDq//

edge impurity transport study in stochastic layer of lhd and scrape-off layer of hl-2a

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